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How many perfect squares less than 1000 have a ones digit of 2, 3 or 4?

 May 29, 2020
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Since there are only 32 numbers to try:  02,  12,  22, 32, ..., 312  (322 is larger than 1000), it would be easiest just to try them all.

However, if you want a little more orgainized way, you might consider this:

What is the result when the

--  one's digit is a 1?       1

--  one's digit is a 2?       4                             x

--  one's digit is a 3?       9

--  one's digit is a 4?       6

--  one's digit is a 5?       5

--  one's digit is a 6?       6

--  one's digit is a 7?       9

--  one's digit is an 8?     4                              x

--  one's digit is a 9?       1

 

So the question becomes:  How many numbers smaller than 32 have a one's digit which is either a "2" or an "8"?

 May 30, 2020

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